If `x` is a rational number and `y` is an irrational number, then both `x\ +\ y\ a n d\ x y` are necessarily rational both `x\ +\ y\ a n d\ x y` are necessarily irrational `x y` is necessarily irrational, but `x\ +\ y` can be either rational or irrational `x\ +\ y` is necessarily irrational, but `x y` can be either rational or irrational

Explanation

No. (xy) is necessarily an irrational only when `x ne O`.
Let x be a non-zero rational and y be an irrational. Then , we have to show that xy be an irrational . If possible, let xy be a rational number. Since, quotient of two non- zero rational so , `((xy)/x)` is a rational number
` Rgihtarrow ` Y is a rational number .
But, this contradicts the fact that y is an irrational number. thus, our supposition is wrong. Hence , xy is an irrational number. but, when x=0, then xy=0, rational number.